Our kitchen sink drainage pipe which leads to our basement (this pipe goes out to our drywell/cesspool) appears to be broken about 3 feet beyond our original foundation wall (where we have a basement) under a new kitchen area slab. Please suggest the best way to get this repaired. Do we need to break up the kitchen floor (please “no”), or can we go to it through the original basement foundation wall. There also appears to be another drainage pipe about 3 feet parallel to this one that leads out to the same drywell. It handles our laundry, etc. Can we attach the kitchen drainage to this in the basement and bypass the broken pipe altogether. Any suggestions, info will be appreciated.

When our nseptic systems went in back in the 50's the washer and kitchen sink discharge first went to a grease trap before the liquid went to the septic tank. You ask,"Can we attach the kitchen drainage to this in the basement and bypass the broken pipe altogether?"
I would say, yes you can. Simply cap off the broken kitchen drain and connect to the laundry drain. Good luck, Tom